Blade shape creation program and method

ABSTRACT

In a blade shape creation program and method, a blade thickness function defining equation is constructed by a cubic function as a first function defining a leading edge blade thickness function on a leading edge side of a maximum blade thickness point of the blade thickness function, and a cubic function as a second function defining a trailing edge blade thickness function on a trailing edge side of the maximum blade thickness point; is defined, with a camber line length, a position of maximum blade thickness, a maximum blade thickness value, a leading edge blade thickness change rate, a trailing edge blade thickness change rate, a leading edge blade thickness value, and a trailing edge blade thickness value being taken as design factors, and has a boundary condition that the first function and the second function have tangents continuous with each other at the maximum blade thickness point.

CROSS REFERENCE TO RELATED APPLICATION

The entire disclosure of Japanese Patent Application No. 2004-099031filed on Mar. 30, 2004, including specification, claims, drawings andsummary, is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a blade shape creation program and method forcreating the blade shape of a cooling fan or the like.

2. Description of the Related Art

When the blade shape of a cooling fan installed in a vehicle is to becreated (drawn) in designing the cooling fan, for example, the firststep is to create (draw) the cross-sectional shapes of a blade at aplurality of locations in the hub diameter direction of the blade. Then,based on these cross-sectional shapes of the blade, the entire shape ofthe blade (visible outline and exterior surface) is created (drawn) byspline interpolation or the like. A method using “Joukowski airfoil”shown, for example, in the following document is named as one ofordinary methods for drawing the cross-sectional shape of the blade:

-   -   T. Fujimoto, “2nd Revision of Fluid Dynamics”, 2nd Revision, 6th        Edition, YOKENDO Co., Ltd., published Jan. 20, 1992, p. 141”

An outline of this method will be shown in FIGS. 11(a) and 11(b). The“Joukowski airfoil” is an airfoil (cross-sectional shape of blade) 3 asshown in FIG. 11(b), which is obtained by-the coordinate transformation(mapping) of a combination of two circles 1 and 2 with centers M and M′,as shown in FIG. 11(a), by the equation (1) offered below. To change theairfoil profile (cross-sectional shape of blade) in this case, theshapes of the two circles 1 and 2 before coordinate transformation areadjusted. The method using “Joukowski airfoil” is one of general methodsfor drawing an “average camber curve (camber line)”, which is a basicskeleton of the cross-sectional shape of the blade. According to thismethod, the central points of the airfoil (cross-sectional shape ofblade) 3 shown in FIG. 11(b) are connected to draw a camber line 4.$\begin{matrix}{{z = {\zeta + \frac{a^{2}}{\zeta}}},{a = \frac{c}{4}}} & (1)\end{matrix}$

To improve the performance of the blade (lift performance and dragperformance), it is necessary to change (adjust) the shape of thesection of the blade contour (airfoil) (i.e., blade profile), and studyinfluence on the performance of the blade. For this purpose, it iseffective to individually change (adjust) a plurality of design factors(details to be described later), which determine the blade profile,thereby directly investigating the degree of contribution of each designfactor to the performance of the blade. Particularly, the ability tochange each design factor, independently of one another, on the leadingedge side of a maximum blade thickness point (see FIG. 3, details to bedescribed later) of a blade thickness function, which represents achange in the blade thickness at a section of the blade, and on thetrailing edge side of the maximum blade thickness point would be veryeffective for studying the performance of the blade.

However, conventional methods, such as the method using “Joukowskiairfoil”, pose difficulty in changing each design factor independently.Needless to say, changing each design factor, independently on theleading edge side and the trailing edge side of the blade thicknessfunction, is also difficult.

The present invention has been accomplished in light of theabove-described circumstances. It is an object of the present inventionto provide a blade shape creation program and method capable of changinga plurality of design factors, which determine the blade profile(airfoil), on the leading edge side and the trailing edge side of theblade thickness function, with the leading edge side and the trailingedge side being separated from each other, in changing (adjusting) theairfoil.

It is another object of the present invention to provide a blade shapecreation program and method capable of changing a plurality of designfactors, which determine the blade profile (airfoil), independently onthe leading edge side and the trailing edge side of the blade thicknessfunction, in changing (adjusting) the airfoil, and also capable ofreliably checking the created airfoil based on numerical values, withoutrelying on visual checks.

SUMMARY OF THE INVENTION

A first aspect of the present invention, for attaining the above object,is a blade shape creation program for creating a blade shape on a spacevirtually defined by a computer, wherein a blade thickness functiondefining equation for defining a blade thickness function representing achange in a blade thickness to be defined on a-cross section of theblade shape is constructed by a first function which defines a leadingedge blade thickness function on a leading edge side of a maximum bladethickness point of the blade thickness function, and a second functionwhich defines a trailing edge blade thickness function on a trailingedge side of the maximum blade thickness point of the blade thicknessfunction.

A second aspect of the present invention is the blade shape creationprogram according to the first aspect, wherein the blade thicknessfunction defining equation has the first function and the secondfunction each defined by a cubic function, is defined, with a camberline length of a section of the blade shape, a position of maximum bladethickness, a maximum blade thickness value, a leading edge bladethickness change rate, a trailing edge blade thickness change rate, aleading edge blade thickness value, and a trailing edge blade thicknessvalue being taken as design factors, and has a boundary condition thatthe first function and the second function have tangents continuous witheach other at the maximum blade thickness point.

A third aspect of the present invention is a blade shape creation methodfor creating a blade shape on a virtually defined space, wherein a bladethickness function defining equation for defining a blade thicknessfunction representing a change in a blade thickness to be defined on across section of the blade shape is constructed by a first functionwhich defines a leading edge blade thickness function on a leading edgeside of a maximum blade thickness point of the blade thickness function,and a second function which defines a trailing edge blade thicknessfunction on a trailing edge side of the maximum blade thickness point ofthe blade thickness function.

A fourth aspect of the present invention is the blade shape creationmethod according to the third aspect, wherein the blade thicknessfunction defining equation has the first function and the secondfunction each defined by a cubic function, is defined, with a camberline length of a section of the blade shape, a position of maximum bladethickness, a maximum blade thickness value, a leading edge bladethickness change rate, a trailing edge blade thickness change rate, aleading edge blade thickness value, and a trailing edge blade thicknessvalue being taken as design factors, and has a boundary condition thatthe first function and the second function have tangents continuous witheach other at the maximum blade thickness point.

A fifth aspect of the present invention is a blade shape creationprogram for creating a blade shape on a space virtually defined by acomputer, wherein a blade thickness function defining equation fordefining a blade thickness function representing a change in a bladethickness to be defined on a cross section of the blade shape isconstructed by a first function which defines a leading edge bladethickness function on a leading edge side of a maximum blade thicknesspoint of the blade thickness function, and a second function whichdefines a trailing edge blade thickness function on a trailing edge sideof the maximum blade thickness point of the blade thickness function;and in the first function and the second function of the blade thicknessfunction defining equation, a value of the blade thickness is calculatedover an entire region of the blade thickness function, and thecalculated blade thickness value is compared with a maximum bladethickness value set as a design factor to check whether the bladethickness function has a blade thickness value larger than the maximumblade thickness value.

A sixth aspect of the present invention is a blade shape creationprogram for creating a blade shape on a space virtually defined by acomputer, wherein a blade thickness function defining equation fordefining a blade thickness function representing a change in a bladethickness to be defined on a cross section of the blade shape isconstructed by a first function which defines a leading edge bladethickness function on a leading edge side of a maximum blade thicknesspoint of the blade thickness function, and a second function whichdefines a trailing edge blade thickness function on a trailing edge sideof the maximum blade thickness point of the blade thickness function;and the first function and the second function of the blade thicknessfunction defining equation are differentiated to check over an entireregion of the blade thickness function whether the blade thicknessfunction has a maximum or minimum point or an inflection point at aposition other than a position of maximum blade thickness set as adesign factor.

A seventh aspect of the present invention is the blade shape creationprogram according to the fifth or sixth aspect, wherein the bladethickness function defining equation has the first function and thesecond function each defined by a cubic function, is defined, with acamber line length of a section of the blade shape, a position ofmaximum blade thickness, a maximum blade thickness value, a leading edgeblade thickness change rate, a trailing edge blade thickness changerate, a leading edge blade thickness value, and a trailing edge bladethickness value being taken as design factors, and has a boundarycondition that the first function and the second function have tangentscontinuous with each other at the maximum blade thickness point.

An eighth aspect of the present invention is the blade shape creationprogram according to any one of the fifth to seventh aspects, whereinresults of checking whether the blade thickness function has a bladethickness value larger than the maximum blade thickness value, orresults of checking whether the blade thickness function has a maximumor minimum point or an inflection point at a position other than theposition of maximum blade thickness are displayed on a checklist window.

A ninth aspect of the present invention is a blade shape creation methodfor creating a blade shape on a virtually defined space, wherein a bladethickness function defining equation for defining a blade thicknessfunction representing a change in a blade thickness to be defined on across section of the blade shape is constructed by a first functionwhich defines a leading edge blade thickness function on a leading edgeside of a maximum blade thickness point of the blade thickness function,and a second function which defines a trailing edge blade thicknessfunction on a trailing edge side of the maximum blade thickness point ofthe blade thickness function; and in the first function and the secondfunction of the blade thickness function defining equation, a value ofthe blade thickness is calculated over an entire region of the bladethickness function, and the calculated blade thickness value is comparedwith a maximum blade thickness value set as a design factor to checkwhether the blade thickness function has a blade thickness value largerthan the maximum blade thickness value.

A tenth aspect of the present invention is a blade shape creation methodfor creating a blade shape on a virtually defined space, wherein a bladethickness function defining equation for defining a blade thicknessfunction representing a change in a blade thickness to be defined on across section of the blade shape is constructed by a first functionwhich defines a leading edge blade thickness function on a leading edgeside of a maximum blade thickness point of the blade thickness function,and a second function which defines a trailing edge blade thicknessfunction on a trailing edge side of the maximum blade thickness point ofthe blade thickness function; and the first function and the secondfunction of the blade thickness function defining equation aredifferentiated to check over an entire region of the blade thicknessfunction whether the blade thickness function has a maximum or minimumpoint or an inflection point at a position other than a position ofmaximum blade thickness set as a design factor.

An eleventh aspect of the present invention is the blade shape creationmethod according to the ninth or tenth aspect, wherein the bladethickness function defining equation has the first function and thesecond function each defined by a cubic function, is defined, with acamber line length of a section of the blade shape, a position ofmaximum blade thickness, a maximum blade thickness value, a leading edgeblade thickness change rate, a trailing edge blade thickness changerate, a leading edge blade thickness value, and a trailing edge bladethickness value being taken as design factors, and has a boundarycondition that the first function and the second function have tangentscontinuous with each other at the maximum blade thickness point.

A twelfth aspect of the present invention is the blade shape creationmethod according to any one of the ninth to eleventh aspects, whereinresults of checking whether the blade thickness function has a bladethickness value larger than the maximum blade thickness value, orresults of checking whether the blade thickness function has a maximumor minimum point or an inflection point at a position other than theposition of maximum blade thickness are displayed on a checklist.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given hereinbelow and the accompanying drawingswhich are given by way of illustration only, and thus are not limitativeof the present invention, and wherein:

FIG. 1 is an external outline view of a personal computer for executinga blade shape creation program according to an embodiment of the presentinvention;

FIG. 2A is a front view of a cooling fan, and FIG. 2B is a side view ofthe cooling fan (a view taken in the direction of A in FIG. 2A);

FIG. 3 is an explanation drawing of design factors for determining ablade profile (airfoil), and a coordinate system (blade thicknessfunction drawing method) used when drawing a blade thickness function bya cubic function;

FIG. 4 is a view showing an example of drawing the blade thicknessfunction when only a leading edge blade thickness change rate ischanged;

FIG. 5 is a view showing an example of drawing a blade thicknessfunction in which the blade thickness value of a blade thickness pointother than a set maximum blade thickness point is greater than themaximum blade thickness value of the maximum blade thickness point;

FIG. 6 is a view showing an example of drawing a blade thicknessfunction which has inflection points at blade thickness points otherthan a set maximum blade thickness point;

FIG. 7 is a view showing an example in which a blade section extendsbeyond a hub;

FIG. 8 is a view showing an example of a checklist window;

FIG. 9 is a view showing an example of drawing a blade thicknessfunction of a shape in which there is no problem in a maximum bladethickness value;

FIG. 10 is a view showing an example of drawing a blade thicknessfunction of a delicate shape in which the blade thickness value of ablade thickness point other than a set maximum blade thickness point isslightly greater than the maximum blade thickness value of the maximumblade thickness point; and

FIG. 11 is an explanation drawing showing a method of drawing a bladeprofile with the use of “Joukowski airfoil”.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present invention will now be described in detailwith reference to the accompanying drawings. The application of theblade shape creation program according to the present invention to thecreation of the blade shape of a cooling fan will be taken as an examplefor explanation.

FIG. 1 is an external outline view of a personal computer for executingthe blade shape creation program according to an embodiment of thepresent invention. FIG. 2A is a front view of a cooling fan, and FIG. 2Bis a side view of the cooling fan (a view taken in the direction of A inFIG. 2A).

As shown in FIG. 1, a personal computer 11 has a computer body 12, andperipheral instruments connected to the computer body 12, such as akeyboard 13 as an input means, and a display device 14 as a displaymeans, for example, CRT or a liquid crystal display.

The computer body 12 is equipped with a CPU, a hard disk (HD) drive, anda compact disk (CD) drive, and the CPU executes a blade shape creationprogram P (software) stored in storage media such as HD and CD. Theblade shape creation program P is a program for creating a blade shapeon a space virtually defined by the personal computer 11. This programcan change a plurality of design factors, which determine a bladeprofile (sectional shape of a blade; airfoil), independently of eachother, in changing the blade profile, although details of the programwill be described later.

The keyboard 13 is used to enter data for execution of the blade shapecreation program P into the computer body 12. The display device 14 isused for displaying on a display screen 15 the data entered from thekeyboard 13 into the computer body 12, and the results of execution ofthe blade shape creation program P in the computer body 12. For example,the display device 14 displays a checklist window 16 (details to bedescribed later).

FIGS. 2A and 2B show an example of a cooling fan loaded on a vehicle. Acooling fan 21 illustrated in FIGS. 2A and 2B comprises a plurality of(eight in the illustrate example) blades 23 provided on an outerperipheral surface 22 a of a cylindrical hub 22. The cooling fan 21 hasa rotating shaft (not shown) connected, for example, to a rotating shaftof an engine of the vehicle, and rotationally driven thereby. In theside view of FIG. 2B, each blade 23 is provided on the outer peripheralsurface 22 a of the hub such that its chord is inclined at apredetermined blade inclination angle with respect to a hub center axisB (see FIG. 7). The exterior shape of the blade 23 is not limited to theillustrated one, but is available in various types.

In creating (drawing) the blade shape of each blade 23 of the coolingfan 21 for designing the cooling fan 21, the present embodiment isarranged to execute the blade shape creation program P on the personalcomputer 11, thereby deriving a blade thickness function representing achange in the blade thickness in a blade section, and creating (drawing)a blade profile having a blade thickness calculated by the bladethickness function in connection with a separately designated camberline.

The blade thickness function creation capability (program), bladethickness function checking capability (program), and checklist windowdisplay capability (program) of the blade shape creation program P willbe described in detail based on FIGS. 3 to 10.

FIG. 3 is an explanation drawing of design factors for determining ablade profile (airfoil), and a coordinate system (blade thicknessfunction drawing method) used when drawing a blade thickness function bya cubic function. FIG. 4 is a view showing an example of drawing theblade thickness function when only a leading edge blade thickness changerate is changed. FIG. 5 is a view showing an example of drawing anairfoil and a blade thickness function in which the blade thicknessvalue of a blade thickness point other than a set maximum bladethickness point is greater than the maximum blade thickness value of themaximum blade thickness point. FIG. 6 is a view showing an example ofdrawing and airfoil and a blade thickness function which have inflectionpoints at blade thickness points other than a set maximum bladethickness point. FIG. 7 is a view showing an example in which a bladesection extends beyond a hub. FIG. 8 is a view showing an example of achecklist window. FIG. 9 is a view showing an example of drawing anairfoil and a blade thickness function of a shape in which there is noproblem in a maximum blade thickness value. FIG. 10 is a view showing anexample of drawing an airfoil and a blade thickness function of adelicate shape in which the blade thickness value of a blade thicknesspoint other than a set maximum blade thickness point is slightly greaterthan the maximum blade thickness value of the maximum blade thicknesspoint.

The blade thickness function creation capability of the blade shapecreation program P will be described first of all.

In providing the blade thickness function creation (drawing) capability,the following seven design factors (1) to (7) were selected as optimal(basic) design factors for determining the blade profile (airfoil) (seeFIG. 3):

-   -   (1) Camber line length Lc    -   (2) Position of maximum blade thickness x_(Tmax)    -   (3) Maximum blade thickness value y_(Tmax)    -   (4) Leading edge blade thickness change rate α    -   (5) Trailing edge blade thickness change rate β    -   (6) Leading edge blade thickness value Tf    -   (7) Trailing edge blade thickness value Tb

As shown in FIG. 3, a camber line 31 is a line formed by connecting thecenters of blade thicknesses B of a blade section (airfoil) 32, and acamber line length Lc refers to the length of the camber line 31. Theblade thickness B of the blade section 32 is a blade thickness in adirection perpendicular to a tangent to the camber line 31 at eachcamber point SP on the camber line 31. A blade thickness function 33represents a change in the blade thickness B, namely, a change over therange from a leading edge 31 a of the camber line 31 (leading edge 32 aof the blade section 32) to a trailing edge 31 b of the camber line 31(trailing edge 32 b of the blade section 32). The leading edge 31 a ofthe camber line 31 is a site where airflow enters, while the trailingedge 31 b of the camber line 31 is a site where airflow exits.

To express the blade thickness function 33 by an x-y coordinate system,a coordinate axis representing the position of the camber line 31 in thecamber line length direction is designated as an x-axis, the leadingedge 31 a of the camber line 31 is taken as the origin of the x-axis,and a coordinate axis representing the magnitude of the blade thicknessB is designated as a y-axis. A maximum blade thickness value y_(Tmax) isthe maximum value of the blade thickness B. Each point on the bladethickness function 33 is called a blade thickness point BP and, of theseblade thickness points BP's, the point at which the blade thickness Btakes the maximum blade thickness value y_(Tmax) is called a maximumblade thickness point BPM. In the x-y coordinate system, the bladethickness B is expressed by the y-coordinate, and refers to the lengthof a perpendicular dropped from each blade thickness point BP on theblade thickness function 33 to the x-axis. The position of maximum bladethickness x_(Tmax) is the position in the camber line direction (x-axisdirection) at which the blade thickness B takes the maximum bladethickness value y_(Tmax).

A leading edge blade thickness change rate α is the change rate of theblade thickness B at the leading edge 33 a of the blade thicknessfunction 33, and refers to an angle which a tangent 33 c at the leadingedge 33 a of the blade thickness function 33 makes with a line 34 aparallel to the x-axis. A trailing edge blade thickness change rate β isthe change rate of the blade thickness B at the trailing edge 33 b ofthe blade thickness function 33, and refers to an angle which a tangent33 d at the trailing edge 33 b of the blade thickness function 33 makeswith a line 34 b parallel to the x-axis. A leading edge blade thicknessvalue Tf is the value of the blade thickness B at the leading edge 33 aof the blade thickness function 33. The leading edge blade thicknessvalue Tf may be zero when a leading edge portion of the blade section 32is arcuate. Alternatively, the leading edge blade thickness value Tf maybe some value when the leading edge portion is flat, as in theillustrated example. A trailing edge blade thickness value Tb is thevalue of the blade thickness B at the trailing edge 33 b of the bladethickness function 33. The trailing edge blade thickness value Tb may bezero when a trailing edge portion of the blade section 32 is at an acuteangle. Alternatively, the trailing edge blade thickness value Tb may besome value when the trailing edge portion is flat, as in the illustratedexample.

An equation for defining the blade thickness function 33, whichrepresents a change in the blade thickness B to be defined on the crosssection 32 of the blade shape, is constructed by a first function whichdefines a leading edge blade thickness function on the leading edge sideof the maximum blade thickness point BPM of the blade thickness function33, and a second function which defines a trailing edge blade thicknessfunction on the trailing edge side of the maximum blade thickness pointBPM on the blade thickness function 33. That is, as shown in FIG. 3, theblade thickness function 33 is divided into a leading edge side and atrailing edge side, with the maximum blade thickness point BPM as aboundary. A cubic function of an equation (2) is selected as a firstfunction which defines (represents) a leading edge blade thicknessfunction 33A on the leading edge side of the maximum blade thicknesspoint BPM, while a cubic function of an equation (3) is selected as asecond function which defines (represents) a trailing edge bladethickness function 33B on the trailing edge side of the maximum bladethickness point BPM.y _(L) =a _(L) x _(L) ³ +b _(L) x _(L) ² +c _(L) x _(L) +d _(L)   (2)y _(T) =a _(T) x _(T) ³ +b _(T) x _(T) ² +c _(T) x _(T) +d _(T)   (3)

The reason for selecting the cubic functions as the first function andthe second function is that the aforementioned seven design factors areselected as the optimal design factors determining the shape of theblade section 32 (the shape of the blade thickness function 33), wherebythe eight constraints (1) to (8) to be indicated below can be set basedon these design factors. That is, of the following eight constraints (1)to (8), the four constrains (1), (3), (5) and (7) can be set for theleading edge side of the blade thickness function 33, while the otherfour constrains (2), (4), (6) and (8) can be set for the trailing edgeside of the blade thickness function 33. In accordance with theseconstraints, therefore, the respective coefficients (a_(L), b_(L),c_(L), d_(L), a_(T), b_(T), C_(T), d_(T)) of the cubic functions of theequations (2) and (3) can all be uniquely determined. The constrains (1)to (4) are the constraints concerned with the transit points of theblade thickness function 33, while the constraints (5) to (8) are theconstraints about the gradient of the tangents at the transit points ofthe blade thickness function 33.

If the number of the design factors (constraints) is small, quadraticfunctions may be used as the first and second functions. If the numberof the design factors (constraints) is large, functions of fourth orhigher order may be used. However, if the number of the design factors(constraints) is small, sufficient adjustment of an airfoil cannot bemade. Too large a number of the design factors (constraints) wouldwastefully render the equations of the functions complicated. Thus, itwould be best to select, as the first function and the second function,cubic functions which are suitable for the seven design factors (camberline length Lc, position of maximum blade thickness x_(Tmax), maximumblade thickness value y_(Tmax), leading edge blade thickness change rateα, trailing edge blade thickness change rate β, leading edge bladethickness value Tf, trailing edge blade thickness value Tb) optimal asdesign factors for determining the blade profile (airfoil).

-   -   (1) When x_(L)=0, y_(L)=Tf: Leading edge position (leading edge        blade thickness value)    -   (2) When x_(T)=Lc, y_(T)=Tb: Trailing edge position (camber line        length, trailing edge blade thickness value)    -   (3) When x_(L)=x_(Tmax), y_(L)=y_(Tmax): Position of maximum        blade thickness, maximum blade thickness value    -   (4) When x_(T)=x_(Tmax), y_(T)=y_(Tmax): Position of maximum        blade thickness, maximum blade thickness value    -   (5) When x_(L)=0, dy_(L)/dx_(L)=tan α: Leading edge blade        thickness change rate    -   (6) When x_(T)=Lc, dy_(T)/dx_(T)=tan(−β): Trailing edge blade        thickness change rate    -   (7) When x_(L)=x_(Tmax), dy_(L)/dx_(L)=0: Position of maximum        blade thickness (gradient of tangent)    -   (8) When x_(T)=x_(Tmax), dy_(T)/dx_(T)=0: Position of maximum        blade thickness (gradient of tangent)

The constraint (1) is a constraint on the leading edge position of theblade thickness function 33 (leading edge blade thickness value Tf) forthe equation (2). When x_(L)=0, namely, at the position of the leadingedge 33 a of the blade thickness function 33, the blade thickness valuey_(L)=Tf. The constraint (2) is a constraint on the trailing edgeposition of the blade thickness function 33 (camber line length Lc,trailing edge blade thickness value Tb) for the equation (3). Whenx_(T)=Lc (camber line length), namely, at the position of the trailingedge 33 b of the blade thickness function 33, the blade thickness valuey_(T)=Tb. The constraint (3) is a constraint on the position of maximumblade thickness x_(Tmax) and the maximum blade thickness value y_(Tmax)of the blade thickness function 33 for the equation (2). The constraint(4) is a constraint on the position of maximum blade thickness x_(Tmax)and the maximum blade thickness value y_(Tmax) of the blade thicknessfunction 33 for the equation (3). The constraint (5) is a constraint onthe leading edge blade thickness change rate α of the blade thicknessfunction 33 for the equation (2), namely, a constraint on the gradientof the tangent at the position of the leading edge 33 a of the bladethickness function 33. The constraint (6) is a constraint on thetrailing edge blade thickness change rate β of the blade thicknessfunction 33 for the equation (3), namely, a constraint on the gradientof the tangent at the position of the trailing edge 33 b of the bladethickness function 33.

The constraint (7) is a constraint on the gradient of the tangent at theposition of maximum blade thickness x_(Tmax), i.e., at the maximum bladethickness point BPM of the blade thickness function 33, for the equation(2). The constraint (8) is a constraint on the gradient of the tangentat the position of maximum blade thickness x_(Tmax), i.e., at themaximum blade thickness point BPM of the blade thickness function 33,for the equation (3). Under the constrains (7) and (8), the gradient ofthe tangent at the position of maximum blade thickness x_(Tmax) (maximumblade thickness point BPM) is zero, i.e., dy_(L)/dx_(L)=0. This isbecause unless the gradient of the tangent at the position of maximumblade thickness x_(Tmax) (maximum blade thickness point BPM) is zero,the value of the blade thickness B (y_(L), y_(T)) at the set maximumblade thickness point BPM is not maximal. The constrains (7) and (8)also mean that the maximum blade thickness value at the position ofmaximum blade thickness x_(Tmax) (maximum blade thickness point BPM) issimilarly y_(Tmax), and the gradient of the tangent (dy_(L)/dx_(L),dy_(T)/dx_(T)) is similarly zero, showing that the equation (2) of thefirst function and the equation (3) of the second function have theboundary condition that their tangents are continuous with each other atthe maximum blade thickness point BPM.

Based on the above constraints (1) to (8), the respective design factors(camber line length Lc, position of maximum blade thickness x_(Tmax),maximum blade thickness value y_(Tmax), leading edge blade thicknesschange rate α, trailing edge blade thickness change rate β, leading edgeblade thickness value Tf, trailing edge blade thickness value Tb) areset (changed) independently of each other to find the respectivecoefficients (a_(L), b_(L), c_(L), d_(L), a_(T), b_(T), c_(T), d_(T)) ofthe cubic functions of the equations (2) and (3). By so doing, theleading edge blade thickness function 33A can be defined (drawn) basedon the cubic function of the equation (2), and the trailing edge bladethickness function 33B can be defined (drawn) based on the cubicfunction of the equation (3). By combining the cubic functions of theequations (2) and (3), the whole of the blade thickness function 33 canbe defined (drawn).

The relationships between the respective coefficients (a_(L), b_(L),c_(L), d_(L), a_(T), b_(T), c_(T), d_(T)) of the cubic functions of theequations (2) and (3) and the respective design factors (camber linelength Lc, position of maximum blade thickness x_(Tmax), maximum bladethickness value y_(Tmax), leading edge blade thickness change rate α,trailing edge blade thickness change rate β, leading edge bladethickness value Tf, trailing edge blade thickness value Tb) are asindicated by the equations (4) to (11) offered below. To avoid thecomplexity of the indications of the equations, the equations (9), (10)and (11) for b_(T), c_(T) and d_(T) include a_(T). However, since a_(T)is a function involving only the design factors as in the equation (8),b_(T), c_(T) and d_(T) can also be regarded as functions composed of thedesign factors alone.

As the following equations (4) to (7) show, the respective coefficients(a_(L), b_(L), c_(L), d_(L)) of the equation (2) for the cubic functionon the leading edge side can be uniquely determined by determining theposition of maximum blade thickness x_(Tmax), maximum blade thicknessvalue y_(Tmax), leading edge blade thickness change rate α, and leadingedge blade thickness value Tf as the design factors. As the followingequations (8) to (11) show, the respective coefficients (a_(T), b_(T),c_(T), d_(T)) of the equation (3) for the cubic function on the trailingedge side can be uniquely determined by determining the camber linelength Lc, position of maximum blade thickness x_(Tmax), maximum bladethickness value y_(Tmax), trailing edge blade thickness change rate β,and trailing edge blade thickness value Tb as the design factors. Theprocedure for deriving the following relational expressions (4) to (11)will be described later. $\begin{matrix}{a_{L} = \frac{{{- 2}y_{T\quad\max}} + {{x_{T\quad\max} \cdot \tan}\quad\alpha} + T_{f}}{x_{T\quad\max}^{3}}} & (4) \\{b_{L} = {\frac{y_{T\quad\max} - T_{f}}{x_{T\quad\max}^{2}} - \frac{\tan\quad\alpha}{x_{T\quad\max}} - {x_{T\quad\max}( \frac{\begin{matrix}{{{- 2}y_{T\quad\max}} + {x_{T\quad\max} \cdot}} \\{{\tan\quad\alpha} + T_{f}}\end{matrix}}{x_{T\quad\max}^{3}} )}}} & (5) \\{c_{L} = {\tan\quad\alpha}} & (6) \\{d_{L} = T_{f}} & (7) \\{a_{T} = {- \frac{{( {L_{c} - x_{T\quad\max}} ) \cdot {\tan( {- \beta} )}} + {2y_{T\quad\max}} - {2T_{b}}}{( {x_{T\quad\max} - L_{c}} )^{3}}}} & (8) \\{b_{T} = {{{- \frac{3}{2}}{( {L_{c} + x_{T\quad\max}} ) \cdot a_{T}}} + \frac{\tan( {- \beta} )}{2( {L_{c} - x_{T\quad\max}} )}}} & (9) \\{c_{T} = {{a_{T} \cdot ( {{\frac{1}{2}L_{c}^{2}} + {2{L_{c} \cdot x_{T\quad\max}}} + {\frac{1}{2}x_{T\quad\max}^{2}}} )} -}} & (10) \\{\quad{\frac{1}{L_{c} - x_{T\quad\max}}( {\frac{( {L_{c} + x_{T\quad\max}} ) \cdot {\tan( {- \beta} )}}{2} + y_{T\quad\max} - T_{b}} )}} & \quad \\{d_{T} = {{\frac{1}{6}{( {x_{T\quad\max}^{3} - {2{x_{T\quad\max} \cdot L_{c}^{2}}} - {5{x_{T\quad\max}^{2} \cdot L_{c}}}} ) \cdot a_{T}}} +}} & (11) \\{\quad{\frac{x_{T\quad\max}}{x_{T\quad\max} - L_{c}}\begin{pmatrix}{\frac{x_{T\quad\max} \cdot {\tan( {- \beta} )}}{6} -} \\{{\frac{2}{3}( {\frac{( {L_{c} + x_{T\quad\max}} ) \cdot {\tan( {- \beta} )}}{2} + y_{T\quad\max} - T_{b}} )} +} \\{\frac{x_{T\quad\max} - L_{c}}{x_{T\quad\max}}y_{T\quad\max}}\end{pmatrix}}} & \quad\end{matrix}$

The blade thickness function 33, which has been created (drawn) by thecubic functions of the equations (2) and (3), is combined with thecamber line 31 created (drawn) beforehand. That is, the values of theblade thickness B (y_(L), y_(T)) at the respective blade thicknesspoints BP of the blade thickness function 33 are added to the respectivecamber points SP of the camber line 31 in a direction perpendicular tothe tangents at the respective camber points SP. As a result, the shapeof the blade section 32 is created (drawn). Such a shape of bladesection (blade profile) is created (drawn) at each of a plurality oflocations in the hub diameter direction of the blade. Based on theresulting blade profiles, spline interpolation is performed to create(draw) a spline curve (visible outline of the blade) and a splinesurface (exterior surface of the blade), thereby creating (drawing) theentire shape of the blade (external diameter line, external diametersurface). In this case, the camber line 31 may be created by theaforementioned method using the “Joukowski airfoil”, or may be createdby any method.

According to the present embodiment, as described above, under the bladeshape creation program P, which creates a blade shape on a spacevirtually defined by the personal computer 11, the equation for definingthe blade thickness function 33, which represents a change in the bladethickness B to be defined on the section 32 of the blade shape iscomposed of the first function (cubic function) which defines theleading edge blade thickness function 33A on the leading edge side ofthe maximum blade thickness point BPM of the blade thickness function33, and the second function (cubic function) which defines the trailingedge blade thickness function 33B on the trailing edge side of themaximum blade thickness point BPM of the blade thickness function 33.Thus, with the exception of the design factors concerning the maximumblade thickness point at the boundary between the first function and thesecond function (i.e., position of maximum blade thickness x_(Tmax),maximum blade thickness value y_(Tmax)), the design factors on theleading edge side of the blade thickness function 33 and those on thetrailing edge side of the blade thickness function 33 can beindependently set (changed) by the first function and the secondfunction. Thus, the influence of each design factor on the site of flowcan be systematically studied. This facilitates tuning of the site offlow, and enables an airfoil of higher performance to be developed. Inconnection with the maximum blade thickness point BPM on the boundarybetween the first function and the second function, it goes withoutsaying that the first function and the second function are equal to eachother in terms of the position of maximum blade thickness x_(Tmax) andthe maximum blade thickness value y_(Tmax), with their tangents at BPMcontinuing, and the gradients of the tangents being zero.

In the present embodiment, in particular, the seven design factors(camber line length Lc, position of maximum blade thickness x_(Tmax),maximum blade thickness value y_(Tmax), leading edge blade thicknesschange rate α, trailing edge blade thickness change rate β, leading edgeblade thickness value Tf, trailing edge blade thickness value Tb) wereselected as optimal design factors for determining the blade profile(airfoil) and the cubic functions of the equations (2) and (3) wereselected as the first function and the second function suited for thesedesign factors. Thus, the respective design factors can be changedindependently of each other. This makes it possible to directly graspthe degree of influence which each design factor exerts on theperformance of the blade (lift performance and drag performance) (i.e.,the degree of contribution to blade performance).

For example, FIG. 4 shows an example of the blade thickness function 33created (drawn), with only the leading edge blade thickness change rateα being changed in three different ways, and an example of the bladesection 32 created (drawn) based on the blade thickness function 33 andthe camber line 31. In FIG. 4, only the leading edge blade thicknesschange rate α is changed, and the other design factors (camber linelength Lc, position of maximum blade thickness x_(Tmax), maximum bladethickness value y_(Tmax), trailing edge blade thickness change rate β,leading edge blade thickness value Tf, trailing edge blade thicknessvalue Tb) are not changed. Thus, the influence of the leading edge bladethickness change rate α on the performance of the blade can be graspeddirectly. Since each design factor can be changed independently of oneanother in this manner, the influence of each design factor on the siteof flow can be systematically studied. Hence, tuning of the site of flowbecomes easy, and an airfoil with higher performance can be developed.

The procedure for deriving the relationships between the respectivecoefficients (a_(L), b_(L), c_(L), d_(L), a_(T), b_(T), c_(T), d_(T)) inthe cubic functions of the equations (2) and (3) and the design factors(camber line length Lc, position of maximum blade thickness x_(Tmax),maximum blade thickness value y_(Tmax), leading edge blade thicknesschange rate α, trailing edge blade thickness change rate β, leading edgeblade thickness value Tf, trailing edge blade thickness value Tb) willbe shown.

First, the relations between the respective coefficients (a_(L), b_(L),c_(L), d_(L)) of the cubic function equation (2) on the leading edgeside of the blade thickness function and the design factors are derivedin accordance with the following procedure:

From the equation (2) and the constraint (1),d_(L)=T_(f)   (12)

From the equation (2),dy _(L) /dx _(L)=3a _(L) x _(L) ²+2b _(L) x _(L) +c _(L)   (13)

From the equation (13) and the constrain (5),c_(L)=tan α  (14)

From the equation (2) and the constraint (3), the equation (12) and theequation (14),y _(Tmax) =a _(L) ·x _(Tmax) ³ +b _(L) ·x _(Tmax) ² +x _(Tmax)·tan α+T_(f)   (15)

Both sides are multiplied by 2 to give2y _(Tmax)=2a _(L) ·x _(Tmax) ³+2b _(L) ·x _(Tmax) ²+2x _(Tmax)·tan α+T_(f)   (16)

From the equation (13) and the equation (14), as well as the constraint(7),0=3a _(L) ·x _(Tmax) ²+2b _(L) ·x _(Tmax)+tan α  (17)

Both sides are multiplied by x_(Tmax) to obtain0=3a _(L) ·x _(Tmax) ³+2b _(L) ·x _(Tmax) ² +x _(Tmax)·tan α  (18)

Subtraction of the equation (18) from the equation (16) gives2y _(Tmax) =−a _(L) ·x _(Tmax) ³ +x _(Tmax)·tan α+T _(f) $\begin{matrix}{{\therefore a_{L}} = \frac{{{- 2}y_{T\quad\max}} + {{x_{T\quad\max} \cdot \tan}\quad\alpha} + T_{f}}{x_{T\quad\max}^{3}}} & (19)\end{matrix}$

From the equation (15), $\begin{matrix}{b_{L} = {{\frac{y_{T\quad\max} - T_{f}}{x_{T\quad\max}^{2}} - \frac{\tan\quad\alpha}{x_{T\quad\max}} - {a_{L} \cdot x_{T\quad\max}}}\quad = {\frac{y_{T\quad\max} - T_{f}}{x_{T\quad\max}^{2}} - \frac{\tan\quad\alpha}{x_{T\quad\max}} - \quad{x_{T\quad\max}( \frac{{{- 2}y_{T\quad\max}} + {{x_{T\quad\max} \cdot \tan}\quad\alpha} + T_{f}}{x_{T\quad\max}^{3}} )}}}} & (20)\end{matrix}$

Next, the relations between the respective coefficients (a_(T), b_(T),c_(T), d_(T)) of the cubic function equation (3) on the trailing edgeside of the blade thickness function and the design factors are derivedin accordance with the following procedure:

From the equation (3),dy _(T) /dx _(T)=3a _(T) ·x _(T) ²+2b _(T) ·x _(T) +c _(T)   (21)

From the equation (21) and the constraint (6)tan(−β)=3a _(T) ·L _(c) ²+2b _(T) ·L _(c) +c _(T)   (22)

From the equation (21) and the constraint (8),0=3a _(T) ·x _(Tmax) ²+2b _(T) ·x _(Tmax) +c _(T)   (23)

Subtraction of the equation (23) from the equation (22) gives$\begin{matrix}{{\tan( {- \beta} )} = {{{{3{a_{T} \cdot ( {L_{c}^{2} - x_{T\quad\max}^{2}} )}} + {2{b_{T} \cdot ( {L_{c} - x_{T\quad\max}} )}}}\therefore b_{T}} = {{{- \frac{3}{2}}{( {L_{c} + x_{T\quad\max}} ) \cdot a_{T}}} + \frac{\tan( {- \beta} )}{2( {L_{c} - x_{T\quad\max}} )}}}} & (24)\end{matrix}$

From the equation (3) and the constraint (2),T _(b) =a _(T) ·L _(c) ³ +b _(T) ·L _(c) ² +c _(T) ·L _(c) +d _(T)  (25)

From the equation (3) and the constraint (4),y _(Tmax) =a _(T) ·x _(Tmax) ³ +b _(T) ·x _(Tmax) ² +c _(T) ·x _(Tmax)+d _(T)   (26)

Subtraction of the equation (26) from the equation (25) givesT _(b) −y _(Tmax) =a _(T)·(L _(c) ³ −x _(Tmax) ³)+b _(T)·(L _(c) ² −x_(Tmax) ²)+c _(T)·(L _(c) −x _(Tmax))   (27)

Substitution of the equation (24) into the equation (27), followed byarrangement, yields $\begin{matrix}{{\therefore c_{T}} = {{a_{T} \cdot ( {{\frac{1}{2}L_{c}^{2}} + {2{L_{c} \cdot x_{T\quad\max}}} + {\frac{1}{2}x_{T\quad\max}^{2}}} )} - \quad{\frac{1}{L_{c} - x_{T\quad\max}}( {\frac{( {L_{c} + x_{T\quad\max}} ) \cdot {\tan( {- \beta} )}}{2} + y_{T\quad\max} - T_{b}} )}}} & (28)\end{matrix}$

Subtraction of (the equation (26)×3) from (the equation (23)×x_(Tmax))gives $\begin{matrix}{d_{T} = {{{- \frac{x_{T\quad\max}^{2}}{3}}b_{T}} - {\frac{2x_{T\quad\max}}{3}c_{T}} + y_{T\quad\max}}} & (29)\end{matrix}$

Substitution of b_(T) and c_(T) into the equation (29) followed byarrangement, yields $\begin{matrix}{{\therefore d_{T}} = {{\frac{1}{6}{( {x_{T\quad\max}^{3} - {2{x_{T\quad\max} \cdot L_{c}^{2}}} - {5{x_{T\quad\max}^{2} \cdot L_{c}}}} ) \cdot a_{T}}} + \quad{\frac{x_{T\quad\max}}{x_{T\quad\max} - L_{c}}( {\frac{x_{T\quad\max} \cdot {\tan( {- \beta} )}}{6} - \quad{\frac{2}{3}( {\frac{( {L_{c} + x_{T\quad\max}} ) \cdot {\tan( {- \beta} )}}{2} + y_{T\quad\max} - T_{b}} )} + \quad{\frac{x_{T\quad\max} - L_{c}}{x_{T\quad\max}}y_{T\quad\max}}} )}}} & (30)\end{matrix}$

Substitution of b_(T), c_(T) and d_(T) into the equation (23), followedby arrangement, yields $\begin{matrix}{{\therefore a_{T}} = {- \frac{{( {L_{c} - x_{T\quad\max}} ) \cdot {\tan( {- \beta} )}} + {2y_{T\quad\max}} - {2T_{b}}}{( {x_{T\quad\max} - L_{c}} )^{3}}}} & (31)\end{matrix}$

Next, the blade thickness function checking capability and the checklistwindow display capability in the blade shape creation program P will bedescribed.

In creating (drawing) the blade thickness function 33 by the blade shapecreation program P (cubic functions of the equations (2) and (3)), thefollowing cases may be encountered, depending on a combination of theseven design factors (camber line length Lc, position of maximum bladethickness x_(Tmax), maximum blade thickness value y_(Tmax), leading edgeblade thickness change rate α, trailing edge blade thickness change rateβ, leading edge blade thickness value Tf, trailing edge blade thicknessvalue Tb) determining the blade profile (airfoil), even if the eightconstraints (1) to (8) to be satisfied are fulfilled: There may be ablade thickness function, like the blade thickness function 33illustrated in FIG. 5, which, at a blade thickness point BP other than aset maximum blade thickness point BPM, has a value of blade thickness B(y_(L), x_(L)) greater than a maximum blade thickness value y_(Tmax) atthe set maximum blade thickness point BPM. There may be another bladethickness function, like the blade thickness function 33 illustrated inFIG. 6, which, at blade thickness points BP other than the set maximumblade thickness point BPM, has inflection points (may have a maximum orminimum point).

Under the blade shape creation program P, therefore, a numerical checkis made for such cases (i.e., whether a blade thickness value greaterthan the set maximum blade thickness value is present, and whether amaximum or minimum point or an inflection point is present at a bladethickness point other than the set maximum blade thickness point) at thetime of creating the blade thickness function 33. A further check isperformed of whether the blade section 32 does not extend beyond the hub22. The results of these checks are displayed on the checklist window. Aconcrete procedure is as follows:

<Method of Checking Whether a Blade Thickness Value Greater than a SetMaximum Blade Thickness Value is Present>

In the first function (cubic function) and the second function (cubicfunction) of the blade thickness function defining equation, whosecoefficients were determined by setting the design factors(constraints), the value of the blade thickness B (y_(L), x_(L)) iscalculated over the entire region of the blade thickness function 33 inthe camber line direction (x-axis direction of FIG. 3). That is, inconnection with the cubic function of the equation (2), each coefficientis determined based on the design factors (constrains), and then a bladethickness value y_(L) at each position (each blade thickness point BP)over the range from x_(L)=0 to x_(L)=x_(Tmax) is calculated. Inconnection with the cubic function of the equation (3) as well, eachcoefficient is determined based on the design factors (constrains), andthen a blade thickness value y_(T) at each position (each bladethickness point BP) over the range from x_(T)=x_(Tmax) to x_(T)=Lc iscalculated.

These calculated blade thickness values y_(L) and y_(T) are comparedwith the maximum blade thickness value y_(Tmax) set as a design factorto check whether the blade thickness function 33 has blade thicknessvalues y_(L) and y_(T) greater than the maximum blade thickness valuey_(Tmax).

<Method of Checking Whether a Maximum, Minimum or Inflection Point otherthan a Set Maximum Blade Thickness Point is Present>

The first function (cubic function) and the second function (cubicfunction) of the blade thickness function defining equation, whosecoefficients were determined by setting the design factors(constraints), are subjected to differentiation (differentiation offirst order, or differentiation of second or higher order). By so doing,whether the blade thickness function 33 has a maximum or minimum pointor an inflection point at a position other than the position of maximumblade thickness x_(Tmax) (blade thickness point BP other than themaximum blade thickness point BPM) set as a design factor is checkedover the entire region of the blade thickness function 33.

For example, in the first function (cubic function) and the secondfunction (cubic function) of the blade thickness function definingequation, whose coefficients were determined by setting the designfactors (constraints), the gradient of the tangent to the bladethickness function 33 (dy_(L)/dx_(L), dy_(T)/dx_(T)) is calculated overthe entire region of the blade thickness function 33 in the camber linedirection (x-axis direction of FIG. 3). That is, in connection with thecubic function of the equation (2), each coefficient is determined basedon the design factors (constrains), and then the gradient of the tangent(dy_(L)/dx_(L)) at each position (each blade thickness point BP) overthe range from x_(L)=0 to x_(L)=x_(Tmax) is calculated. In connectionwith the cubic function of the equation (3) as well, each coefficient isdetermined based on the design factors (constrains), and then thegradient of the tangent (dy_(T)/dx_(T)) at each position (each bladethickness point BP) over the range from x_(T)=x_(Tmax) to x_(T)=Lc iscalculated. Then, a check is made of whether the positivity ornegativity of the sign of the calculated gradient of the tangent(dy_(L)/dx_(L), dy_(T)/dx_(T)) is reversed before and after a positionother than the set position of maximum blade thickness (blade thicknesspoint BP other than the maximum blade thickness point BPM) (namely,whether there is a maximum or minimum point).

<Method for Checking Whether the Blade Section Does Not Extend Beyondthe Hub>

A check is made of whether the blade section 32, created (drawn) basedon the blade thickness function 33 by the blade thickness functiondefining equation (cubic function), does not extend beyond the hub 22 ina side view (plan view), when its inclination angle with respect to thehub center axis B is also taken into consideration. FIG. 7 shows anexample in which a leading edge portion C of the blade section 32extends beyond the hub 22 in a side view (plan view) of the cooling fan.

<Method for Display of Checklist Window>

The results of the checks made by the above checking methods aredisplayed on a checklist window 16 on a display screen 15 as shown inFIG. 8. Curve-1 to Curve-3 in a column of the checklist window 16represent blade thickness functions created (drawn) for the bladesection at each position of the blade in the hub diameter direction. Thenumber of the created blade thickness functions is not limited to 3 inthe illustrated example, but may be 2 or 4 or more in accordance withthe shape of the blade to be created.

Error-1 to Error-4 in a row of the checklist window 16 represent itemschecked by the above-described checking methods. Error-1 shows theresults of the check of whether the blade thickness function 33 as awhole has a blade thickness value greater than the set maximum bladethickness value. When values y_(L) and y_(T) greater than the maximumblade thickness value y_(Tmax) are not present, a judgment “no problem”is made, and a circle “◯” meaning no problem is displayed. If bladethickness values y_(L) and y_(T) greater than the maximum bladethickness value y_(Tmax) are present, this means that the conditions forsetting (preconditions) the maximum blade thickness value and theposition of maximum blade thickness are not fulfilled. Since a judgment“problematical” is made, “warning” is displayed.

Error-2 shows the results of the check of whether the leading edge bladethickness function 33A has a maximum or minimum point or an inflectionpoint. When there is no maximum or minimum point or no inflection point,a judgment “no problem” is made, and a circle “◯” meaning no problem isdisplayed. If there is a maximum or minimum point or an inflectionpoint, the presence of a maximum or minimum point or an inflection pointon the leading edge side (leading edge blade thickness function 33A) isconsidered to affect, often adversely, the performance of the blade.Thus, a judgment “problematical” is made, and “warning” is displayed.Error-3 shows the results of the check of whether the trailing edgeblade thickness function 33B has a maximum or minimum point or aninflection point. When there is no maximum or minimum point or noinflection point, a judgment “no problem” is made, and a circle “◯”meaning no problem is displayed. If there is a maximum or minimum pointor an inflection point, “caution” is displayed. The reason why“caution”, rather than “warning,” is displayed here is that the presenceof a maximum or minimum point or an inflection point on the trailingedge side (trailing edge blade thickness function 33B) does notnecessarily exert an adverse influence on the performance of the blade,but is rather considered to exert a favorable influence on theperformance of the blade. Anyway, a display of “caution” enables thedeveloper to recognize reliably that a maximum or minimum point or aninflection point is present.

Error-4 shows the results of the check of whether the blade section 32does not extend beyond the hub 22. When the blade section 32 does notextend beyond the hub 22, a judgment “no problem” is made, and a circle“◯” meaning no problem is displayed. If the blade section 32 extendsbeyond the hub 22, this is not necessarily a problem, and it suffices tohave the developer recognize that the blade section 32 extends beyondthe hub 22. Thus, “caution” is displayed.

A “Close” button 42 displayed on the display screen 16 of FIG. 8 is abutton to be pushed (for example, to be clicked by a mouse) for closing(erasing) the checklist window 16.

According to the present embodiment described above, in the firstfunction (cubic function) and the second function (cubic function) ofthe blade thickness function defining equation, the value of the bladethickness B (y_(L), y_(T)) is calculated over the entire region of theblade thickness function 33. This calculated blade thickness value(y_(L), y_(T)) is compared with the maximum blade thickness valuey_(Tmax) set as a design factor to check whether the blade thicknessfunction 33 has a blade thickness value (y_(L), y_(T)) greater than themaximum blade thickness value y_(Tmax). Hence, the presence or absenceof a delicate blade thickness value (y_(L), y_(T)), which is difficultto confirm visually, can be numerically checked with reliability whencreating the blade thickness function 33. Thus, the efficiency of bladedevelopment increases. For example, the blade thickness function 33 ofFIG. 9 poses no problem about blade thickness values. In regard to theblade thickness function 33 of FIG. 10, on the other hand, a value ofthe blade thickness B (y_(L)) at a blade thickness point BP nearer tothe leading edge is slightly larger than a maximum blade thickness valuey_(Tmax) at the set maximum blade thickness point BPM. The problem ofsuch a delicate blade thickness value (y_(L)) can be checked reliably.

According to the present embodiment, moreover, the first function (cubicfunction) and the second function (cubic function) of the bladethickness function defining equation are differentiated. By so doing,whether the blade thickness function 33 has a maximum or minimum pointor an inflection point at a position other than the position of maximumblade thickness set as a design factor is checked over the entire regionof the blade thickness function 33. Hence, the presence or absence of amaximum or minimum point or an inflection point, which is difficult toconfirm visually, can be numerically checked with reliability whencreating the blade thickness function 33. Thus, the efficiency of bladedevelopment increases.

According to the present embodiment, moreover, the results of the checksof whether the blade thickness function has a greater blade thicknessvalue than the maximum blade thickness value, whether the bladethickness function has a maximum or minimum point or an inflection pointat a blade thickness point other than the maximum blade thickness point,and whether the blade section does not extend beyond the hub aredisplayed on the checklist window 16. Accordingly, these checkingresults are clear at a glance, and the efficiency of blade developmentincreases.

While the present invention has been described by the above embodiment,it is to be understood that the invention is not limited thereby, butmay be varied or modified in many other ways. Such variations ormodifications are not to be regarded as a departure from the spirit andscope of the invention, and all such variations and modifications aswould be obvious to one skilled in the art are intended to be includedwithin the scope of the appended claims.

1. A blade shape creation program for creating a blade shape on a spacevirtually defined by a computer, wherein a blade thickness functiondefining equation for defining a blade thickness function representing achange in a blade thickness to be defined on a cross section of theblade shape is constructed by a first function which defines a leadingedge blade thickness function on a leading edge side of a maximum bladethickness point of the blade thickness function, and a second functionwhich defines a trailing edge blade thickness function on a trailingedge side of the maximum blade thickness point of the blade thicknessfunction.
 2. The blade shape creation program according to claim 1,wherein the blade thickness function defining equation has the firstfunction and the second function each defined by a cubic function, isdefined, with a camber line length of a section of the blade shape, aposition of maximum blade thickness, a maximum blade thickness value, aleading edge blade thickness change rate, a trailing edge bladethickness change rate, a leading edge blade thickness value, and atrailing edge blade thickness value being taken as design factors, andhas a boundary condition that the first function and the second functionhave tangents continuous with each other at the maximum blade thicknesspoint.
 3. A blade shape creation method for creating a blade shape on avirtually defined space, wherein a blade thickness function definingequation for defining a blade thickness function representing a changein a blade thickness to be defined on a cross section of the blade shapeis constructed by a first function which defines a leading edge bladethickness function on a leading edge side of a maximum blade thicknesspoint of the blade thickness function, and a second function whichdefines a trailing edge blade thickness function on a trailing edge sideof the maximum blade thickness point of the blade thickness function. 4.The blade shape creation method according to claim 3, wherein the bladethickness function defining equation has the first function and thesecond function each defined by a cubic function, is defined, with acamber line length of a section of the blade shape, a position ofmaximum blade thickness, a maximum blade thickness value, a leading edgeblade thickness change rate, a trailing edge blade thickness changerate, a leading edge blade thickness value, and a trailing edge bladethickness value being taken as design factors, and has a boundarycondition that the first function and the second function have tangentscontinuous with each other at the maximum blade thickness point.
 5. Ablade shape creation program for creating a blade shape on a spacevirtually defined by a computer, wherein a blade thickness functiondefining equation for defining a blade thickness function representing achange in a blade thickness to be defined on a cross section of theblade shape is constructed by a first function which defines a leadingedge blade thickness function on a leading edge side of a maximum bladethickness point of the blade thickness function, and a second functionwhich defines a trailing edge blade thickness function on a trailingedge side of the maximum blade thickness point of the blade thicknessfunction, and in the first function and the second function of the bladethickness function defining equation, a value of the blade thickness iscalculated over an entire region of the blade thickness function, andthe calculated blade thickness value is compared with a maximum bladethickness value set as a design factor to check whether the bladethickness function has a blade thickness value larger than the maximumblade thickness value.
 6. A blade shape creation program for creating ablade shape on a space virtually defined by a computer, wherein a bladethickness function defining equation for defining a blade thicknessfunction representing a change in a blade thickness to be defined on across section of the blade shape is constructed by a first functionwhich defines a leading edge blade thickness function on a leading edgeside of a maximum blade thickness point of the blade thickness function,and a second function which defines a trailing edge blade thicknessfunction on a trailing edge side of the maximum blade thickness point ofthe blade thickness function, and the first function and the secondfunction of the blade thickness function defining equation aredifferentiated to check over an entire region of the blade thicknessfunction whether the blade thickness function has a maximum or minimumpoint or an inflection point at a position other than a position ofmaximum blade thickness set as a design factor.
 7. The blade shapecreation program according to claim 5, wherein the blade thicknessfunction defining equation has the first function and the secondfunction each defined by a cubic function, is defined, with a camberline length of a section of the blade shape, a position of maximum bladethickness, a maximum blade thickness value, a leading edge bladethickness change rate, a trailing edge blade thickness change rate, aleading edge blade thickness value, and a trailing edge blade thicknessvalue being taken as design factors, and has a boundary condition thatthe first function and the second function have tangents continuous witheach other at the maximum blade thickness point.
 8. The blade shapecreation program according to claim 6, wherein the blade thicknessfunction defining equation has the first function and the secondfunction each defined by a cubic function, is defined, with a camberline length of a section of the blade shape, a position of maximum bladethickness, a maximum blade thickness value, a leading edge bladethickness change rate, a trailing edge blade thickness change rate, aleading edge blade thickness value, and a trailing edge blade thicknessvalue being taken as design factors, and has a boundary condition thatthe first function and the second function have tangents continuous witheach other at the maximum blade thickness point.
 9. The blade shapecreation program according to claim 5, wherein results of checkingwhether the blade thickness function has a blade thickness value largerthan the maximum blade thickness value, or results of checking whetherthe blade thickness function has a maximum or minimum point or aninflection point at a position other than the position of maximum bladethickness are displayed on a checklist window.
 10. The blade shapecreation program according to claim 6, wherein results of checkingwhether the blade thickness function has a blade thickness value largerthan the maximum blade thickness value, or results of checking whetherthe blade thickness function has a maximum or minimum point or aninflection point at a position other than the position of maximum bladethickness are displayed on a checklist window.
 11. A blade shapecreation method for creating a blade shape on a virtually defined space,wherein a blade thickness function defining equation for defining ablade thickness function representing a change in a blade thickness tobe defined on a cross section of the blade shape is constructed by afirst function which defines a leading edge blade thickness function ona leading edge side of a maximum blade thickness point of the bladethickness function, and a second function which defines a trailing edgeblade thickness function on a trailing edge side of the maximum bladethickness point of the blade thickness function, and in the firstfunction and the second function of the blade thickness functiondefining equation, a value of the blade thickness is calculated over anentire region of the blade thickness function, and the calculated bladethickness value is compared with a maximum blade thickness value set asa design factor to check whether the blade thickness function has ablade thickness value larger than the maximum blade thickness value. 12.A blade shape creation method for creating a blade shape on a virtuallydefined space, wherein a blade thickness function defining equation fordefining a blade thickness function representing a change in a bladethickness to be defined on a cross section of the blade shape isconstructed by a first function which defines a leading edge bladethickness function on a leading edge side of a maximum blade thicknesspoint of the blade thickness function, and a second function whichdefines a trailing edge blade thickness function on a trailing edge sideof the maximum blade thickness point of the blade thickness function,and the first function and the second function of the blade thicknessfunction defining equation are differentiated to check over an entireregion of the blade thickness function whether the blade thicknessfunction has a maximum or minimum point or an inflection point at aposition other than a position of maximum blade thickness set as adesign factor.
 13. The blade shape creation method according to claim11, wherein the blade thickness function defining equation has the firstfunction and the second function each defined by a cubic function, isdefined, with a camber line length of a section of the blade shape, aposition of maximum blade thickness, a maximum blade thickness value, aleading edge blade thickness change rate, a trailing edge bladethickness change rate, a leading edge blade thickness value, and atrailing edge blade thickness value being taken as design factors, andhas a boundary condition that the first function and the second functionhave tangents continuous with each other at the maximum blade thicknesspoint.
 14. The blade shape creation method according to claim 12,wherein the blade thickness function defining equation has the firstfunction and the second function each defined by a cubic function, isdefined, with a camber line length of a section of the blade shape, aposition of maximum blade thickness, a maximum blade thickness value, aleading edge blade thickness change rate, a trailing edge bladethickness change rate, a leading edge blade thickness value, and atrailing edge blade thickness value being taken as design factors, andhas a boundary condition that the first function and the second functionhave tangents continuous with each other at the maximum blade thicknesspoint.
 15. The blade shape creation method according to claim 11,wherein results of checking whether the blade thickness function has ablade thickness value larger than the maximum blade thickness value, orresults of checking whether the blade thickness function has a maximumor minimum point or an inflection point at a position other than theposition of maximum blade thickness are displayed on a checklist. 16.The blade shape creation method according to claim 12, wherein resultsof checking whether the blade thickness function has a blade thicknessvalue larger than the maximum blade thickness value, or results ofchecking whether the blade thickness function has a maximum or minimumpoint or an inflection point at a position other than the position ofmaximum blade thickness are displayed on a checklist.